Non-Destructive Determination of Single Crystal Elastic Constants in AM Alloys Using Resonant Ultrasound Spectroscopy
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There are several constants which have been devised as numerical representations of the behavior of metals under the action of loadings which stress the metal within the range of elastic action. Some of these constants, such as Young's modulus of elasticity in tension and compression, shearing modulus of elasticity, and Poisson's ratio, are regularly used in engineering calculations. Precise tests and experience indicate that these elastic constants are practically unaffected by many of the factors which influence the other mechanical properties of materials and that a few careful determinations under properly controlled conditions are more useful and reliable than many determinations made under less favorable conditions. It is the purpose of this paper to outline the methods employed by the Aluminum Research Laboratories for the determination of some of these elastic constants, to list the values that have been determined for some of the wrought aluminum alloys, and to indicate the variations in the values that may be expected for some of the commercial products of these alloys.
Adiabatic elastic constants of molybdenum-rich rhenium alloys, studying concentration effects on bulk modulus, Debye temperatures and interatomic forces
Dependence of elastic constants of titanium alloys on composition and structure
Dilatational wave velocities and dynamic elastic moduli of Ni-Mn alloys
Solid-state low-temperature elastic properties have been experimentally studied at the NBS Cryogenic Division for four years. Most studies were between room temperature and liquid-helium temperature; some were only to liquid-nitrogen temperature. Two dynamic (high-frequency) experimental methods were used, pulse-echo and resonance, resulting in adiabatic elastic constants. The present paper reviews these studies for 47 technological materials - metals, alloys, and composites. The elastic constants primarily discussed are Young's modulus, the shear modulus, the bulk modulus (reciprocal compressibility), and Poisson's ratio. A summary table is presented to show which base metals tend to exhibit regular, irregular, or anomalous behavior in their elastic constant/temperature curves.
The superconducting properties of single crystals of Nb and two alloys of Nb with Mo were investigated by ultrasonic techniques. The results of measurements of the ultrasonic attenuation and velocities as a function of temperature, Mo composition, crystallographic direction, and ultrasonic frequency are reported. The attenuation and small velocity changes associated with the superconductivity of the samples are shown to be dependent on the sample resistivity ratio which varied from 4.3 for Nb-9% Mo to 6500 for pure Nb. The ultrasonic attenuation data are analyzed in terms of the superconducting energy gap term of the BCS theory. A new model is proposed for the analysis of ultrasonic attenuation in pure superconductors with two partially decoupled energy bands. To analyze the attenuation in pure superconducting Nb, the existence of two energy gaps was assumed to be associated with the two partially decoupled energy bands. One of the gaps was found to have the normal BCS value of 3.4 and the other gap was found to have the anomalously large value of 10. No experimental evidence was found to suggest that the second energy gap had a different transition temperature. The interpretation of the results for the Nb-Mo alloys is shown to be complicated by the possible existence of a second superconducting phase in Nb-Mo alloys with a transition temperature of 0.35 of the transition temperature of the first phase. The elastic constants of Nb and Nb-Mo alloys are shown to be approximately independent of Mo composition to nine atomic percent Mo. These results do not agree with the current microscopic theory of transition temperature for the transition elements.
Aluminum alloys of types 1100, 3003, 5052, 6061, and 2024 were used to study the sensitivity of the acousto-elastic constant to changes in the microstructure. Results show that there is a strong relationship between the acousto-elastic constants and the yield strength and hardness. This relationship depends on whether the alloy is strain hardened or precipitation hardened. In strain hardened alloys, the constants increase as the amount of solid solution is decreased, while the behavior is the opposite in precipitation hardened alloys.
Acoustoelastic constants are calculated for two-phase alloys containing dilute concentrations of precipitates in a solid-solution matrix, on the basis of a model in which the precipitates are represented as a dilute elastic suspension of spherical particle inclusions in an infinite matrix. The longitudinal propagation velocity in the alloy is thereby obtained in terms of the precipitates' concentration and the elastic moduli of the two phases. Results are presented which indicate that the acoustoelastic constant of longitudinal waves in a dilute two-phase alloy varies linearly with the concentration of second-phase precipitates, in agreement with recent measurements in aluminum and steel alloys where the acoustoelastic constants changed linearly with the second phase's volume fraction.
An analytical rationale for the sensitivity-insensitivity of dispersion-strengthened systems to process history is provided. In particular, the research was focussed upon the influence of the particle-matrix interface bond in TD-Nickel and TD-Nichrome, and the manner in which the differences in both elastic constants and thermal expansion coefficients between these phases stress this interface when these alloys are subjected to mechanical and thermal loads upon the mechanical properties of these alloys.
The sensitivity of the velocity of ultrasonic waves to the elasticity of the materials (acousto-elastic constant - AEC) as controlled by the microstructure of the materials was examined experimentally. Rolled-plate specimens of five different Al alloys were subjected to tensile tests while being monitored for the velocity change of a 10 MHz longitudinal wave as a function of the applied tensile stress. The acoustic propagation velocity was measured perpendicularly to the stress. Determinations were made of the yield strength and the hardnesses of the specimens. Samples of the plate materials examined microscopically to characterize the solid phases. The AECs varied linearly with the percentage of solid solution phase of the alloys. The trend for strain-hardened samples was, however, opposite from that in the precipitation-hardened alloys. The results underscore the necessity of considering the microstructural dependencies of the AECs when using ultrasonic NDE methods, and also opened the potential of determining some mechanical properties with NDE techniques.
The behavior of higher order elastic properties, which are much more sensitive to material state than are second order properties, has been studied for steel alloys AISI 1016, 1045, 1095, and 8620 by measuring the stress derivative of the acoustic natural velocity to determine the stress acoustic constants (SAC's). Results of these tests show a 20 percent linear variation of SAC's with carbon content as well as even larger variations with prestrain (plastic deformation). The use of higher order elastic characterization permits quantitative evaluation of solids and may prove useful in studies of fatigue and fracture.
The effect of a zirconium addition (0.05 at. pct) to a stoichiometric NiAl alloy on the brittle-to-ductile transition temperature (BDTT) of this alloy was investigated. Constant velocity tensile tests were conducted to fracture between 300 and 1100 K under initial strain rate 0.00014/sec, and the true stress and true strain values were determined from plots of load vs time after subtracting the elastic strain. The inelastic strain was measured under a traveling microscope. Microstructural characterization of as-extruded and fractured specimens was carried out by SEM and TEM. It was found that, while the addition of 0.05 at. pct Zr strengthened the NiAl alloy, it increased its BDTT; this shift in the BDTT could not be attributed either to variations in grain size or to impurity contents. Little or no room-temperature ductility was observed for either alloy.
The creep and stress rupture behavior of the mechanically alloyed oxide dispersion strengthened nickel-base alloy MA 754 was studied at 760, 982 and 1093 C. Tensile specimens with a fine, highly elongated grain structure, oriented parallel and perpendicular to the longitudinal grain direction were tested at various stresses in air under constant load. It was found that the apparent stress dependence was large, with power law exponents ranging from 19 to 33 over the temperature range studied. The creep activation energy, after correction for the temperature dependence of the elastic modulus, was close to but slightly larger than the activation energy for self diffusion. Rupture was intergranular and the rupture ductility as measured by percentage elongation was generally low, with values ranging from 0.5 to 16 pct. The creep properties are rationalized by describing the creep rates in terms of an effective stress which is the applied stress minus a resisting stress consistent with the alloy microstructure. Values of the resisting stress obtained through a curve fitting procedure are found to be close to the values of the particle by-pass stress for this oxide dispersion strengthened alloy, as calculated from the measured oxide particle distribution.
The objective of this paper is to evaluate, both experimentally and analytically, the appropriate forms of the hardening evolution equations in unified constitutive models for conditions involving nonisothermal loading. Critical experiments were performed for a cast nickel-base superalloy by using variable temperature tensile, creep, and cyclic tests in the 538-982 C temperature range. These experimental results were compared with both isothermal data and predictions of the Bodner-Partom-Bodner, 1987 elastic-viscoplastic theory to assess the effects of thermal history on constitutive behavior. The results indicate that the hardening evolution equations based on isothermal data are applicable for nonisothermal loading of these precipitation strengthened alloys. Additional thermal history effect terms in the hardening evolution equations were not required beyond those accounting for the variation of material constants with temperature. Using material constants determined solely from isothermal data, the inelastic deformation behavior of B1900 + Hf subject to thermomechanical loading were adequately predicted by the Bodner-Partom model.
The objective is to study the effects of constraint on fatigue crack growth under aircraft spectrum loading. A plasticity-induced crack-closure model that accounts for constraint variations during the transition from flat-to-slant crack growth was used to correlate crack-growth rate data under constant-amplitude loading and to calculate crack growth under simulated aircraft spectrum loading. The model was applied to several thin-sheet aluminum alloy materials. Under laboratory air conditions, the transition was shown to be related to the size of the cyclic plastic zone based on the effective stress-intensity factor range for several sheet materials and thicknesses. Results from three-dimensional, elastic-plastic, finite-element analyses of a flat, straight-through crack in a thin-sheet aluminum alloy specimen showed a constraint loss similar to that assumed in the model. Using test data and the closure model, the location of the constraint-loss regime in terms of growth rate and the value of the constraint factor at these rates were determined by trial and error. The model was then used to calculate crack growth under the TWIST spectrum. The calculated results agreed reasonably well with test data. In general, the model predicted shorter crack-growth lives than tests under the TWIST spectrum by about 40 percent. For the TWIST spectrum clipped at Level 3, the calculated lives were within about 20 percent. The results demonstrated that constraint variations, especially for thin-sheet alloys, should be accounted for to predict crack growth under typical aircraft spectra.
An equation for the steady-state rate of creep has been derived by applying the theory of dislocations to the creep of pure metals. The form of this equation is in agreement with empirical equations describing creep rates. The theory was also used to predict the dependence of steady-state rate of creep on physical constants of the material and good agreement was obtained with data in the literature for pure annealed metals. The rate of creep was found to decrease with increasing modulus of rigidity. This relation suggest that one of the requirements for a heat-resisting alloy is that its matrix be a metal that has a high modulus of rigidity and therefore a high modulus of elasticity.
Efficient temperature ranges are indicated for two high-strength aluminum alloys, two titanium alloys, and three steels for some short-time compression-loading applications at elevated temperatures. Only the effects of constant temperatures and short exposure to temperature are considered, and creep is assumed not to be a factor. The structural efficiency analysis is based upon preliminary results of short-time elevated-temperature compressive stress-strain tests of the materials. The analysis covers strength under uniaxial compression, elastic stiffness, column buckling, and the buckling of long plates in compression or in shear.